Fourteen years after his last Oval Office visit, Pakistani Prime Minister Nawaz Sharif is poised to meet this Wednesday with U.S. President Barack Obama. In between, Sharif was deposed in a 1999 coup and then endured nearly a decade in the political wilderness. His arrival this week in Washington marks another moment of triumph for one of South Asia’s political heavyweights.

The trip is Sharif’s first to Washington during what is now his third stint as Pakistan’s premier and comes at a time when U.S. and Pakistan’s turbulent relations are slowly on the mend. Washington rolled out the red carpet for Sharif’s visit: Secretary of State John Kerry hosted him for a dinner on Sunday; he met with business leaders on Monday; and, on Tuesday, Sharif delivered a standing-room only speech at the U.S. Institute of Peace. “I have come here as the elected leader of Pakistan, a land of ancient civilizations and cultural traditions, but a state still young and aspiring to be a modern, moderate and progressive country,” Sharif told the crowd.

Ties between the U.S. and Pakistan arguably reached a low point in 2011 as the two countries clashed over a range of disputes related to American counter-terrorism operations in the region. First, Central Intelligence Agency operative Raymond Davis reportedly killed two men in Lahore. The resulting anti-American uproar in Pakistan led to his imprisonment for months and the U.S. only negotiated his release after it paid the victims’ families $2.4 million in compensation. Then in May, U.S. Navy Seals killed al-Qaeda supremo Osama bin Laden in an embarrassing raid for the Pakistan government, which saw both its sovereignty infringed and its commitment to the fight against extremism called into question. (Adm. Mike Mullen, a top-ranking American military official, then famously accused Pakistan’s military intelligence agency of abetting al-Qaeda and Taliban activities, of “exporting terror.“) Then, in November of that year, a friendly fire incident with NATO forces along the Afghan border killed dozens of Pakistani soldiers, prompting Pakistan to close U.S. supply routes to Afghanistan.

Relations began to improve in July 2012 when Pakistan reopened the supply routes. Sharif, who was elected this summer, campaigned on a friendlier platform towards the U.S. than the government of his predecessor Asif Ali Zardari, the widower of slain former Prime Minister Benazir Bhutto, a longtime Sharif foe. In late August, a Pakistani court overturned the conviction of Shakil Afridi, a World Health Organization physician who had clandestinely helped the U.S. confirm bin Laden’s location in Abbottabad by running a fake vaccine distribution campaign in the town. Afridi’s arrest and subsequent 33-year sentence had been another source of tension between the two countries.

The Obama Administration began moving this summer to unfreeze $1.6 billion in economic and military assistance that had been halted in 2011; the release of the funds coincided with Sharif’s visit. The Administration has also requested an additional $1.16 billion in assistance to Pakistan in the 2014 budget still pending before Congress. Pakistan’s economy is struggling to get on its feet after years of instability and political dysfunction and its rejuvenation is a priority for the business-friendly Sharif.

In the backdrop, though, remain the harder issues underlying the American military presence across the border in Afghanistan and Washington’s use of drones in the neighboring Pakistani tribal areas, which has led to significant civilian casualties. The U.S. withdrawal from Afghanistan in 2014 presents obvious anxieties for Islamabad, which saw the chaos that consumed its neighbor following the retreat of Soviet occupying forces in the 1980s. At the same time, there is a clear desire in Pakistan to no longer be hyphenated in the Western imagination with Afghanistan. “If there is one thing that Sharif should put on the table for joint review, it is the lens through which Pakistan is seen by Washington,” says Sherry Rehman, executive president of the Jinnah Institute, a Pakistani think tank, and, until this summer, Pakistan’s ambassador to the U.S. Ideally, Sharif said in his Tuesday speech, the U.S.-Pakistan relationship would shift its focus on fighting terrorism to preventing it through economic investment and deeper trade ties.

On Sunday, Sharif also asked Kerry to get involved in helping resolve Pakistan’s longstanding with India over the contested territory of Kashmir. “The people of Pakistan want to see all of our issues with India resolved through dialogue,” Sharif said in his speech. “We want to put on a quick track normalizing relations with India.” New Delhi, though, has no interest in American mediation of its disputes with Islamabad, nor is there much indication that the Obama Administration would want to be involved.

Sharif pledged to address all these issues during his 60 minutes with Obama. But no one is holding their breath for a meaningful breakthrough. Washington is still wary of Sharif, who spent his exile in Saudi Arabia, and uncertain of the potential for common ground. “If there is a mismatch between what the interlocutors ask for and how much they believe the other side can give, the talks could well increase mutual resentment,” says Frederic Grare, director and senior associate of the Carnegie Endowment’s South Asia Program. “The result may be a new cycle of tensions that could imperil not only Washington’s short-term goals in Afghanistan but also its broader strategic interests in South Asia.”